Weyl-Heisenberg Frame Operators and Kohn-Nirenberg Symbols

φ-factorable operators and Weyl-Heisenberg frames on LCA groups

Local sampling and approximation of operators with bandlimited Kohn-Nirenberg symbols

Recent sampling theorems allow for the recovery of operators with bandlimited Kohn-Nirenberg symbols from their response to a single discretely supported identifier signal. The available results are inherently non-local. For example, we show that in order to recover a bandlimited operator precisely, the identifier cannot decay in time nor in frequency. Moreover, a concept of local and discrete ...

Local Approximation and Quantization of Operators with Bandlimited Kohn-Nirenberg Symbols

In communiations engineering, the effect of a slowly time-varying communication channel is commonly modeled as a superposition of different translations and modulations. In order to recover signals from the corresponding channel outputs, one first needs to understand how the channel acts on a signal. A mathematical model often used for the effect of such a channel is an operator with a bandlimi...

Analyzing the Weyl-heisenberg Frame Identity

In 1990, Daubechies proved a fundamental identity for WeylHeisenberg systems which is now called the Weyl-Heisenberg Frame Identity. WH-Frame Identity: If g ∈ W (L∞, L), then for all continuous, compactly supported functions f we have: ∑ m,n | < f, EmbTnag > | = 1 b ∑

φ-factorable operators and weyl-heisenberg frames on lca groups